# quadratic form over polynomial rings

If a quadratic form $f(x,y)=ax^2+bxy+cy^{2}$ is defined over a polynomial ring $R(t)$, R is a commutative ring with unity, then, how does a uni modular transformation is defined? Also, what is the matrix associated with this?

Do I get any references on this

• Over a finite field, or over a polynomial ring? How are you defining a quadratic form over a polynomial ring, $a$, $b$, and $c$ are polynomials? – Morgan Rodgers Dec 20 '17 at 7:10
• I edited the question. – thanks Dec 20 '17 at 7:14

The polynomial ring $R[t]$ (not $R(t)$) is, among other things, a commutative ring with unity.